Which of the following numbers is a multiple of 7? ${44,67,96,105,118}$
The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $44 \div 7 = 6\text{ R }2$ $67 \div 7 = 9\text{ R }4$ $96 \div 7 = 13\text{ R }5$ $105 \div 7 = 15$ $118 \div 7 = 16\text{ R }6$ The only answer choice that leaves no remainder after the division is $105$ $ 15$ $7$ $105$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $105$ $105 = 3\times5\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $105$. We can say that $105$ is divisible by $7$.